Faculty of Science AMSI Summer School 2013

Solitons, instantons, Lax pairs and twistors

Omar Foda
The University of Melbourne


This is a series of introductory lectures on nonlinear partial differential equations that can be solved without approximation, and that play a central role in recent studies of non-perturbative phenomena in string and gauge theories.

Course content:

Contact hours

28 hours of hours spread over four weeks, plus consultation as required.



Three short weekly assignments plus a final 3-hour exam


A lecture outline is now available for download.

The primary reference to this set of lectures is the textbook

A copy of the textbook will be put on reserve for students to consult. The precise location where the reserve copy can be found will be decided on by the start of the lectures. Further references will be made available if needed.

Lecture notes that are directly relevant to Weeks 1 and 2 of teaching can be downloaded from Dr Dunajski's Cambridge University website:

Further material, relevant to Weeks 3 and 4, and to the full subject in general, will be made available during the lectures. The lectures will be reasonably self-contained, but a background in basic complex analysis and differential equations is assumed.

Further useful textbooks are

A more advanced reference is

About Omar Foda

I am a mathematical physicist in the department of Mathematics and Statistics, University of Melbourne. My research interests are in classical and quantum integrable model. I am currently interested in applications of integrability to supersymmetric quantum field theories.

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